# Math Help - Integral Curves Equations

1. ## Integral Curves Equations

Question:
For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

I know that y'= 4x + C
But I don't what to do next and how to place these points to find the equation.
Any help io good.
Thanks

2. Originally Posted by Awsom Guy
Question:
For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

I know that y'= 4x + C
But I don't what to do next and how to place these points to find the equation.
Any help io good.
Thanks
find y.

then, use the given points to set up two simultaneous equations to find the arbitrary constants of integration.

3. Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
Thanks

4. Originally Posted by Awsom Guy
Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
Thanks
no, you found y', you need to integrate that to get to y. you will get another arbitrary constant, call it D. then solve for C and D using the points you were given.

5. Do I sub in the x values aswell.

6. Originally Posted by Awsom Guy
Do I sub in the x values aswell.
when you have y, you sub in corresponding x and y values at the same time. your last two equations must only have C and D as unknowns. that's how you'll manage to solve for them

7. but I will have town unknown values C and D how am I meant to figure out the two values:
-12=C+D and
-13=C+D
How does this help.
Thanks

8. Originally Posted by Awsom Guy
but I will have town unknown values C and D how am I meant to figure out the two values:
-12=C+D and
-13=C+D
How does this help.
Thanks
your second equation is not right. and you've solved simultaneous equations before, yeah? That's definitely something you'd have to have done before calculus.

9. What is the second equation then?

10. Originally Posted by Awsom Guy
What is the second equation then?
tell me what expression you got for y

11. I got:
y=2x^2 + C + D.

12. Originally Posted by Awsom Guy
I got:
y=2x^2 + C + D.
it should be $2x^2 + Cx + D$

13. How does that help though

14. Originally Posted by Awsom Guy
How does that help though
fix your second equation now and see.

you can subtract one from the other to start finding your unknowns

15. yes I got it thanks.